5 papers
Metric Fourier approximation of set-valued functions of bounded variation
Elena E. Berdysheva, Nira Dyn, Elza Farkhi +1
We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the parti…
Extending editing capabilities of subdivision schemes by refinement of point-normal pairs
Evgeny Lipovetsky, Nira Dyn
In this paper we extend the 2D circle average of [11] to a 3D binary average of point-normal pairs, and study its properties. We modify classical surface-generating linear subdivis…
Analytic functions in shift-invariant spaces and analytic limits of level dependent subdivision
Maria Charina, Vladimir Yu. Protasov
The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable funct…
Attractors of Trees of Maps and of Sequences of Maps between Spaces with Application to Subdivision
Nira Dyn, David Levin, Peter Massopust
In a previous paper we considered a sequence of maps on a complete metric space and derived an extension of the Banach fixed point theorem. We showed that backward trajecto…
Approximations of Set-Valued Functions by Metric Linear Operators
Nira Dyn, Elza Farkhi, Alona Mokhov
In this work, we introduce new approximation operators for univariate set-valued functions with general compact images. We adapt linear approximation methods for real-valued functi…